Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Dice the potato into small half-inch cubes and cut the chicken breast into uniform bite-sized pieces to ensure even cooking.
In a large mixing bowl, combine the diced chicken, potato cubes, and broccoli florets.
Drizzle the olive oil over the ingredients and sprinkle with garlic powder, onion powder, dried rosemary, sea salt, and black pepper.
Toss the mixture thoroughly until every piece of chicken and vegetable is evenly coated with the oil and spices.
Spread the mixture in a single layer on the prepared baking sheet, making sure not to overcrowd the pan so the potatoes can crisp properly.
Roast for 20 to 25 minutes, tossing the ingredients halfway through the cooking time, until the potatoes are tender and the chicken is golden and cooked through.